一般抛物方程的区域分裂差分方法

对稳定性有影响的一阶项采用中心差分格式,内边界点和各子区域分别对应显隐格式。在一定的稳定性条件下,由最大值原理得出最优收敛结果。最后用数值算例验证方法的实用性。     

抛物方程的一类区域分解迎风差分算法

本文给出了一阶迎风差分、内边界二阶迎风差分和二阶迎风差分三种格式的算法和误差估计。为了减弱稳定性条件限制,先在内边界点上采用小时间步长和大的空间步长进行多层计算,再在内点用隐格式并行计算。这些算法结合了迎风和区域分解的优点,计算格式简单,易于编程实现。     

多孔介质中两相完全可压缩可混溶驱动问题的修正迎风差分法

本文采用修正迎风差分方法处理多孔介质中两相完全可压缩可混溶驱动问题,建立了差分计算格式,并证明了格式的收敛性,同时得到l^2和h^1误差估计,最后数值试验证明了方法的有效性。     

间断系数抛物方程区域分裂有限元方法

考虑了间断系数抛物方程的显隐格式区域分裂有限元方法。在子区域内部应用隐式方法,子区域相邻内边界条件值由一个函数在前层的值给出,从而实现了并行计算。方法在子区域内部和跨越内边界时都保证了问题的守恒性。经过理论分析得到了误差估计度经出了数值算例。     

多孔介质中混溶驱动问题的时空局部网格加密有限差分格式

给出了多孔介质中一维混溶驱动问题在时间和空间上进行局部网格加密的有限差分格式,压力方程采用中心差分格式近似,饱和度方程采用修正迎风格式,且在交界面上采用线性插值,并利用极大值原理给出了误差估计。最后给出了数值算例。     

点源和点汇的混溶驱动问题的特征Galerkin全离散方法

在考虑多孔介质中不可压缩二相混溶驱动问题时，在井口处应用点源和点汇，给出了点源和点汇的混溶驱动问题的数学模型，提出并分析了一类特征Galerkin全离散格式。由于本文考虑在井处用了点源和点汇，由点的奇异性引起压力和浓度的光滑性的减弱，从而得到了比非奇异的源和汇较低阶的收敛率。     

线性互补问题的二级多重分裂并行算法

运用二级迭代方法与矩阵多重分裂理论,同时考虑并行计算,提出了求解线性互补问题的二级多重分裂并行算法。在一定条件下证明了算法的收敛性,分析了算法的收敛速度。该算法与已有算法相比,具有计算量小、计算速度快等特点,因而特别适于求解大规模问题。数值结果表明,该算法是十分有效的。     

油水驱动问题的 Godunov-mixed 方法数值分析

不可压缩油水渗流驱动问题一般由两个方程给出:压力方程和饱和度方程,采用Godunov- mixed方法逼近,即用混合元方法近似压力方程:饱和度方程的对流项用Godunov-flux函数来处理,而扩散项则用混合元来逼进。当流动是光滑分布时可以得到最优阶的估计。     

二维对流扩散方程的二阶精度特征差分格式

针对二维对流扩散方程提出了几类二阶精度特征差分格式,给出了这些格式形成的线性代数方程组可解的充分条件,分析证明了这些格式按离散L^2模是二阶收敛的。最后,具体算例表明这些格式对于对流扩散方程有良好的计算效果。     

基于Allen-Cahn方程图像修复的算子分裂方法（英）

本文提出了一种基于Allen-Cahn方程图像修复的算子分裂方法．其核心思想是利用算子分裂方法将原问题分解为一个线性方程和一个非线性方程,线性方程使用有限差分Crank-Nicolson格式进行离散,非线性方程利用解析方法进行求解,因此时间和空间都能达到二阶精度．由于该方法只作用于图像需要修复的区域,而其余区域的像素值与原始图像的保持一样,可以大大提高计算效率．合成图像和真实图像的数值实验验证了该算法的正确性和有效性．     

二阶强迫非线性时滞差分方程振动的充要条件

给出了二阶强迫非线性时滞差分方程△^2xn anf(xn-k)=gn的所有解弱振动的一个充要条件。     

An efficient parallel procedure for the simulation of crack growth using the cohesive surface methodology

Simulations of crack growth that are based on the cohesive surface methodology typically involve ill‐conditioned systems of equations and require much processing time. This paper shows how these systems of equations can be solved efficiently by adopting the domain decomposition approach in which the finite element mesh is partitioned into multiple blocks. The system of equations is then reduced to a much smaller system of equations that is solved with an iterative algorithm in combination with a powerful two‐level preconditioner. Although the solution algorithm is more efficient than a direct solution algorithm on a single‐processor computer, it becomes really attractive when used on a parallel computer. This is demonstrated for a large scale simulation of crack growth in a polymer using a Cray T3E with 64 processors. Copyright © 2001 John Wiley & Sons, Ltd.     

曲边区域上定常Stokes方程的类Wilson元逼近

本文讨论类Wilson元对曲边区域上定常Stokes方程的有限元逼近,在不需要试探函数u满足divu=0的条件下,克服了由区域变动、边界条件转换、曲边边界逼近以及类Wilson元非协调性等带来的困难,得到了H1-模的最优误差估计。所得结果在弥补以往文献不足的同时,进一步拓宽了类Wilson元的应用范围。     

Time‐parallel implicit integrators for the near‐real‐time prediction of linear structural dynamic responses

The time‐parallel framework for constructing parallel implicit time‐integration algorithms (PITA) is revisited in the specific context of linear structural dynamics and near‐real‐time computing. The concepts of decomposing the time‐domain in time‐slices whose boundaries define a coarse time‐grid, generating iteratively seed values of the solution on this coarse time‐grid, and using them to time‐advance the solution in each time‐slice with embarrassingly parallel time‐integrations are maintained. However, the Newton‐based corrections of the seed values, which so far have been computed in PITA and related approaches on the coarse time‐grid, are eliminated to avoid artificial resonance and numerical instability. Instead, the jumps of the solution on the coarse time‐grid are addressed by a projector which makes their propagation on the fine time‐grid computationally feasible while avoiding artificial resonance and numerical instability. The new PITA framework is demonstrated for a complex structural dynamics problem from the aircraft industry. Its potential for near‐real‐time computing is also highlighted with the solution of a relatively small‐scale problem on a Linux cluster system. Copyright © 2006 John Wiley & Sons, Ltd.     

Proper Generalized Decomposition model reduction in the Bayesian framework for solving inverse heat transfer problems

In this paper, the proper generalized decomposition (PGD) is used for model reduction in the solution of an inverse heat conduction problem within the Bayesian framework. Two PGD reduced order models are proposed and the approximation Error model (AEM) is applied to account for the errors between the complete and the reduced models. For the first PGD model, the direct problem solution is computed considering a separate representation of each coordinate of the problem during the process of solving the inverse problem. On the other hand, the second PGD model is based on a generalized solution integrating the unknown parameter as one of the coordinates of the decomposition. For the second PGD model, the reduced solution of the direct problem is computed before the inverse problem within the parameter space provided by the prior information about the parameters, which is required to be proper. These two reduced models are evaluated in terms of accuracy and reduction of the computational time on a transient three-dimensional two region inverse heat transfer problem. In fact, both reduced models result on substantial reduction of the computational time required for the solution of the inverse problem, and provide accurate estimates for the unknown parameter due to the application of the approximation error model approach.